[mirox]

The problem: A sample containing Na₂HPO₄ and NaH₂PO₄ · 2H₂O weighs 2.15 g. The sample was dissolved in 30 mL HCl (0.1 molar). The excess of HCl is titrated with 8.75 mL NaOH (0.2 molar), using methyl orange as an indicator. Find percent composition of the mixture (by mass).

Attempt: If both the hydrogen- and dihydrogen phosphate are fully protonated to phosphoric  acid. After calculations, this proves not to be logical, as I get a negative result... Also, this approach (which my professor wants) does not make sense to me, as titration with sodium hydroxide solution would lead to deprotonation of phosphoric acid itself, making it impossible to calculate anything.

So the way I approach this is that I can think of it in this manner: upon addition of excess diluted HCl, this happens only:
HPO₄^2- + H⁺  H₂PO₄^-
As the value for this constant it 1/K_a2 = 1.6exp7, you can say the reaction is quantitative, and the existing H₂PO₄^- ion do not interfere the equlibrium.  Basically, it was a fictive buffer all until dissolved in the mineral acid. As methyl orange was used as an indicator, the end point of the titration is when the excess HCl has reacted, so the quantity of hydrogen phosphate ions is: 0.03 mL * 0,1 M -  0.00875 mL * 0.2 M = 0.00125 mol, so the mass of Na₂HPO₄ is 0.1775 g, which is 8.26%.

[Borek]

Methyl orange changes color around pH 4, so yes - at the endpoint solution contains mostly H₂PO₄^-.

Not that I checked the numbers, but the logic looks OK.

It would be interesting to estimate possible errors - for example, at pH 4.0 around 1.4% of the acid is in the H₃PO₄ form. Does it change the result? By how much?

[mirox]

Thank you Borex, your answer is much appreciated, as always. I see what you mean. I don't have the time to do the math now, but yes I see where you are trying to go with this. However, my professor will not accept my answer. I have asked for the solution, but she wants me to figure it out on my own. I am lost, as I have no idea what I should do. She claims that both ions are fully protonated to phosphoric acid. But the numbers don't add up...

[Borek]

This can be a little bit difficult to follow, but I have checked what would be the pH of a solution prepared by mixing 0.1775 g of Na₂HPO₄, 1.972 g of NaH₂PO₄·2H₂O (these are results of your calculations), 30 mL of 0.1 M HCl, 8.75 mL of 0.2 M NaOH, and diluted to 100 mL.

Buffer Maker calculated the pH to be around 4.4, which perfectly fits the idea of the methyl orange endpoint and confirms your calculations fit the information given.